$O(a)$-improved QCD+QED Wilson Dirac operator on GPUs
Anian Altherr, Isabel Campos, Jonathan Coles, Alessandro Cotellucci, Juan Antonio Fernández De la Garza, Roman Gruber, Tim Harris, Javad Komijani, Jens Lücke, S… 展开作者
Anian Altherr, Isabel Campos, Jonathan Coles, Alessandro Cotellucci, Juan Antonio Fernández De la Garza, Roman Gruber, Tim Harris, Javad Komijani, Jens Lücke, Stephanie Maier, Marina Krstić Marinković, Letizia Parato, Agostino Patella, Sara Rosso, Paola Tavella, Hannes Vogt
Markov Chain Monte Carlo simulations of lattice Quantum Chromodynamics (QCD) are the only known tool to investigate non-perturbatively the theory of the strong interaction and are required to perform precision tests of the Standard Model of Particle Physics. As the Markov Chain is a serial process, the sole option for improving the sampling rate is accelerating each individual update step. Heterogeneous clusters of GPU-accelerated nodes offer large total memory bandwidth which can be used to speed-up our application, openQxD-1.1, which is dominated by inversions of the Dirac operator, a large sparse matrix. In this work we investigate offloading the inversion to GPU using the lattice-QCD library QUDA, and our early results demonstrate a significant potential speed-up in the time-to-solution for state-of-the-art problem sizes. Minimal extensions to the existing QUDA library are required for our specific physics programme while greatly enhancing the performance portability of our code and retaining the reliability and robustness of existing applications in openQxD-1.1. Our new interface will enable us to utilize pre-exascale infrastructure and reduce the systematic uncertainty in our physics predictions by incorporating the effects of quantum electromagnetism (QED) in our simulations.
Recent developments have shown that a lot can be gained for QCD simulations from GPU hardware. This can be exploited especially in the case of Ginsparg-Wilson fermions when the com putational costs are particularly high. In this work, we use the Neuberger-Dirac operator as our realisation of Ginsparg-Wilson fermions, which greatly facilitate lattice investigations of decays like $K \to ππ$. We report on the ongoing study of our GPU implementation of the Neuberger-Dirac operator including the exact treatment of the low lying eigenmodes of the Wilson-Dirac operator. Our benchmarks show that we a…
We present an exploratory study of leading isospin breaking effects in mesonic masses using $O(a)$ improved Wilson fermions. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of the light quarks' mass deviations and the electromagnetic coupling. We employ QED$_{\mathrm{L}}$ as a finite volume formulation of QED.
We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and this leads to a severe sign problem. On the other hand simple bags mostly have a positive weight. Since t…
We accelerate many-flavor lattice QCD simulations using multiple GPUs. Multiple pseudo-fermion fields are introduced additively and independently for each flavor in the many-flavor HMC algorithm. Using the independence of each pseudo-fermion field and the blocking technique for the quark solver, we can assign the solver task to each GPU card. In this report we present the blocking technique for the many-flavor dynamical QCD simulations. We investigate the effect of the blocking and the acceleration with the multiple GPUs for the Schrödinger functional simulations with Wilson SU(3) plaquette ga…
Graphical Processing Units (GPUs) are more and more frequently used for lattice QCD calculations. Lattice studies often require computing the quark propagators for several masses. These systems can be solved using multi-shift inverters but these algorithms are memory intensive which limits the size of the problem that can be solved using GPUs. In this paper, we show how to efficiently use a memory-lean single-mass inverter to solve multi-mass problems. We focus on the BiCGstab algorithm for Wilson fermions and show that the single-mass inverter not only requires less memory but also outperform…
We show that maximally twisted mass fermions can be employed to regularize on the lattice the fully unquenched QCD+QED theory with vanishing $θ$-term. We discuss how the critical mass of the up and down quarks can be conveniently determined beyond the electroquenched approximation by imposing that certain symmetries of continuum QCD+QED, which are broken by Wilson terms, get restored in the continuum limit. A mixed action setup is outlined that allows to extend beyond the electroquenched approximation the computation (with only O($a^2$) artifacts) of the leading isospin breaking corrections to…
We present the results of 1+1+1 flavor QCD+QED simulation at the physical point, in which the dynamical quark effects in QED and the up-down quark mass difference are incorporated by the reweighting technique. The physical quark masses together with the lattice spacing are determined with $m_{π^+}$, $m_{K^+}$, $m_{K^0}$ and $m_{Ω^-}$ as physical inputs. Calculations are carried out using a set of 2+1 flavor QCD configurations near the physical point generated by the non-perturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $β=1.9$ on a $32^3\times 64$ lattice. We e…
We present the open-source package openQ*D-1.0, which has been primarily, but not uniquely, designed to perform lattice simulations of QCD+QED and QCD, with and without C* boundary conditions, and O(a) improved Wilson fermions. The use of C* boundary conditions in the spatial direction allows for a local and gauge-invariant formulation of QCD+QED in finite volume, and provides a theoretically clean setup to calculate isospin-breaking and radiative corrections to hadronic observables from first principles. The openQ*D code is based on openQCD-1.6 and NSPT-1.4. In particular it inherits from ope…
Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文学系马尼·L·巴乌米克理论物理研究所）；Transdisciplinary Research Area “Building Blocks of Matter and Fundamental Interactions” (TRA Matter) and Helmholtz Institute for Radiation and Nuclear Physics (HISKP), University of Bonn（波恩大学跨学科研究领域“物质基本组成与基本相互作用”（TRA Matter）及亥姆霍兹辐射与核物理研究所（HISKP））；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所（DESY））；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Computation-Based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究所计算科学与技术研究中心）；Department of Physics, Tsinghua University（清华大学物理系）
The electromagnetic coupling receives significant contributions to its running from non-perturbative QCD effects. We present an update of a lattice QCD study of the Adler function and of its application to the determination of the running of the QED coupling. We perform a high-statistics computation with two flavours of O$(a)$ improved Wilson fermions in a large range of momentum transfer $Q^2$. The running of the electromagnetic coupling, including contributions from $u$, $d$, $s$ and $c$ valence quarks, is compared to phenomenological determinations at intermediate $Q^2$ values. An extension…
We propose a scheme of lattice twisted-mass fermion regularization which is particularly convenient for application to isospin breaking (IB) QCD and QED calculations, based in particular on the so called RM123 approach, in which the IB terms of the action are treated as a perturbation. The main, practical advantage of this scheme is that it allows the calculation of IB effects on some mesonic observables, like e.g. the pi+ - pi0 mass splitting, using lattice correlation functions in which the quark and antiquark fields in the meson are regularized with opposite values of the Wilson parameter r…
Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GP…
Over the past five years, graphics processing units (GPUs) have had a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations in nuclear and particle physics. While GPUs have been applied with great success to the post-Monte Carlo "analysis" phase which accounts for a substantial fraction of the workload in a typical LQCD calculation, the initial Monte Carlo "gauge field generation" phase requires capability-level supercomputing, corresponding to O(100) GPUs or more. Such strong scaling has not been previously achieved. In this contribution, we demonstrate that …
We study the change of the QCD spectrum of low-lying mesons in the presence of an external magnetic field using Wilson fermions in the quenched approximation. Motivated by qualitative differences observed in the spectra of overlap and Wilson fermions for large magnetic fields, we investigate the dependence of the additive quark mass renormalisation on the magnetic field. We provide evidence that the magnetic field changes the critical quark mass both in the free case and on our quenched ensemble. The associated change of the bare quark mass with the magnetic field affects the spectrum and is r…
We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as well as 2d flux loops deformations and breaking, and to observe Wilson-loop area-law.
We present an exploratory study of leading isospin breaking effects in mesonic masses using $O(a)$ improved Wilson fermions with open boundaries. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of deviations in the quark masses and the inverse strong coupling as well as the electromagnetic coupling. We have constructed QED$_{\mathrm{L}}$, which we use as a …
The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using multi-grid algorithms, and due to the throughput improvements brought by GPUs. Deploying hierarchical algorithms optimally on GPUs is non-trivial owing to the lack of parallelism on the coarse grids, and as such, these advances have not proved multiplicative. Using the QUDA library, we demonstrate that by exposing all sources of parallelism that the underlying stenc…
The contribution from hadronic vacuum polarisation effects is responsible for a large fraction of the theoretical uncertainty in the running of the QED coupling. The current level of uncertainty has become a limitation for electroweak precision tests. We use lattice QCD simulations with two flavours of O$(a)$ improved Wilson fermions to determine the Adler function in a broad range of the momentum transfer $Q^2$. The running of the QED coupling, including valence contributions from $u$, $d$, $s$ and $c$ quarks, is compared to phenomenological results at intermediate $Q^2$ values. In the large …
We discuss a mapping of lattice QED with two flavors and a chemical potential to dual variables, which are surfaces for the gauge fields and loops for the fermions. The gauge fields are completely dualized and the corresponding dual variables are integer valued plaquette occupation numbers with constraints that lead to a structure of surfaces that are either closed or bounded by fermion loops. The fermion loops are obtained from a resummed hopping expansion (large mass expansion) of the determinant of the Wilson-Dirac operator. The loops can come with both positive and negative signs. We ident…
We combine techniques previously utilised to study flux tube field density profiles and to study the excited spectrum of the gluonic fields produced by a static quark-antiquark pair. Working with pure gauge SU(3) fields discretised in a lattice, we utilise Wilson loops with a large basis of gluonic spacelike Wilson lines to include different excitations of the quark-antiquark flux tube. To increase the signal over noise ratio, we use the multihit technique in the temporal Wilson lines and the APE smearing in spatial Wilson lines. The number of gluonic operators combined with the space points w…
In this work we explore the performance of CUDA in quenched lattice SU(2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CU…
We present an OpenCL-based Lattice QCD application using a heatbath algorithm for the pure gauge case and Wilson fermions in the twisted mass formulation. The implementation is platform independent and can be used on AMD or NVIDIA GPUs, as well as on classical CPUs. On the AMD Radeon HD 5870 our double precision dslash implementation performs at 60 GFLOPS over a wide range of lattice sizes. The hybrid Monte-Carlo presented reaches a speedup of four over the reference code running on a server CPU.
Quantum fluctuations lead to an anomalous violation of parity symmetry in quantum electrodynamics for an even number of spatial dimensions. While the leading parity-odd electric current vanishes in vacuum, we uncover a non-cancellation of the anomaly for strong electric fields with distinct macroscopic signatures. We perform real-time lattice simulations with fully dynamical gauge fields and Wilson fermions in $2+1$ space-time dimensions. In the static field limit, relevant at early times, we solve the problem analytically. Our results point out the fundamental role of quantum anomalies for st…
We construct a conformal lattice theory with only gauge degrees of freedom based on the induced non-local gauge action in QED$_3$ coupled to large number of flavors $N$ of massless two-component Dirac fermions. This lattice system displays signatures of criticality in gauge observables, without any fine-tuning of couplings and can be studied without Monte Carlo critical slow-down. By coupling exactly massless fermion sources to the lattice gauge model, we demonstrate that non-trivial anomalous dimensions are induced in fermion bilinears depending on the dimensionless electric charge of the fer…
We investigate fermion--anti-fermion production in 1+1 dimensional QED using real-time lattice techniques. In this non-perturbative approach the full quantum dynamics of fermions is included while the gauge field dynamics can be accurately represented by classical-statistical simulations for relevant field strengths. We compute the non-equilibrium time evolution of gauge invariant correlation functions implementing 'low-cost' Wilson fermions. Introducing a lattice generalization of the Dirac-Heisenberg-Wigner function, we recover the Schwinger formula in 1+1 dimensions in the limit of a static…
